Rewrite as a simplified fraction. ${3.5\overline{89} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3589.8989...\\ 10x &= 35.8989...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3554}$ ${x = \dfrac{3554}{990}} $ ${x = \dfrac{1777}{495}} \text{or} {3 \dfrac{292}{495}}$